Manual of plane trigonometry, by J.A. Galbraith and S. Haughton |
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Página 2
... the radius of the circle . The following proportion is evident : 4 ACB : 4 ACU :: arc AB : arc AU . * For an account of the other angular unit , vid . p . 5 . But as ACU is the angular unit , and AU 2 MEASURE OF ANGLES .
... the radius of the circle . The following proportion is evident : 4 ACB : 4 ACU :: arc AB : arc AU . * For an account of the other angular unit , vid . p . 5 . But as ACU is the angular unit , and AU 2 MEASURE OF ANGLES .
Página 3
... evident that 97 must be multiplied by 0.734 , in order to obtain the result . 4. If the radius be 10 feet 9 inches , 0.01347 , calculate the arc . Ans . 71.198 feet . and the angle at the centre Ans . 1.73763 inches . 5. An angle at the ...
... evident that 97 must be multiplied by 0.734 , in order to obtain the result . 4. If the radius be 10 feet 9 inches , 0.01347 , calculate the arc . Ans . 71.198 feet . and the angle at the centre Ans . 1.73763 inches . 5. An angle at the ...
Página 12
... evident that sin 45 ° cos 45 ° , and therefore , = and therefore , I = 2 sin2 45 ° , I = 2 cos2 45 ° ; sin2 45 ° = cos2 45 ° = · If the square root of or 0.5 be extracted to five places of decimals , we find that sin 45 ° = cos 45 ...
... evident that sin 45 ° cos 45 ° , and therefore , = and therefore , I = 2 sin2 45 ° , I = 2 cos2 45 ° ; sin2 45 ° = cos2 45 ° = · If the square root of or 0.5 be extracted to five places of decimals , we find that sin 45 ° = cos 45 ...
Página 41
... evident that an indefinite number of simi- lar triangles may be constructed whose angles shall be equal respectively to three given angles , whose sum is 180 ° . If any other three of the six quan- tities , a , b , c , A , B , C , be ...
... evident that an indefinite number of simi- lar triangles may be constructed whose angles shall be equal respectively to three given angles , whose sum is 180 ° . If any other three of the six quan- tities , a , b , c , A , B , C , be ...
Página 44
... evident that this case is immediately re- duced to the former , for the third angle may be found by subtracting from 180 ° the sum of those which are given . CASE III . Given two sides , and an angle opposite one of the given sides ...
... evident that this case is immediately re- duced to the former , for the third angle may be found by subtracting from 180 ° the sum of those which are given . CASE III . Given two sides , and an angle opposite one of the given sides ...
Otras ediciones - Ver todas
Manual of Plane Trigonometry, by J.A. Galbraith and S. Haughton Joseph Allen Galbraith Sin vista previa disponible - 2016 |
Manual of Plane Trigonometry, by J. A. Galbraith and S. Haughton Joseph Allen Galbraith Sin vista previa disponible - 2015 |
Términos y frases comunes
a² 2bc angle ACB angle is equal angular unit appears from Prop Calculate the value centre Chap circle Circumference complement corresponding number cosec degrees and minutes diameter diff divide equation Euclid Express feet find the angle find the area Find the logarithm find the number Find the product Find the quotient find the value five figures following proportion four figures given angle Given log given side Given the logarithm hypotenuse log cosine log cotangent log sine log tangent Logarithmic Tables mantissa Natural Sines number is equal number of seconds obtain proceed by RULE PROPOSITION rence required to find right angle right-angled triangle secant sect sin A sin sines and cosines square root subtends subtract Tables of Natural tables the corresponding tabular difference triangle BCP TRIGONOMETRICAL MAGNITUDES value of log versin
Pasajes populares
Página ii - RULE. The characteristic of the logarithm of a number greater than unity, is one less than the number of integral figures in the given number.
Página iv - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 5 - ... to be divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are designated respectively, by the characters ° ' ". For example, ten degrees, eighteen minutes, and fourteen seconds, would be written 10° 18
Página 10 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.
Página iv - The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página ii - The Characteristic of the logarithm of a number less than unity, and reduced to the decimal form, is negative and one greater than the number of cyphers following the decimal point.
Página xi - ... will be the logarithm of the quotient. 3°. Find from the Tables the corresponding number. This will be the required quotient.
Página 2 - S3". 6. Besides the above-mentioned unit of angular measure, viz. the 90th part of a right angle, which is always used in practical applications, there is another, viz. the angle at the centre of a circle which is subtended by an arc equal to the radius of the circle, which is more convenient in analytical investigations.
Página 10 - We have, then, that the sine of an angle is equal to the cosine of its complement, and conversely.
Página 29 - Thus: sin (a + a) = sin a cos a + cos a sin a or: sin 2a = 2 sin a cos a...